Searching for effective forces in laboratory insect swarms

James G. Puckett, Douglas H. Kelley, Nicholas T. Ouellette
2014 Scientific Reports  
Collective animal behaviour is often modeled by systems of agents that interact via effective social forces, including short-range repulsion and long-range attraction. We search for evidence of such effective forces by studying laboratory swarms of the flying midge Chironomus riparius. Using multi-camera stereoimaging and particle-tracking techniques, we record three-dimensional trajectories for all the individuals in the swarm. Acceleration measurements show a clear short-range repulsion,
more » ... we confirm by considering the spatial statistics of the midges, but no conclusive long-range interactions. Measurements of the mean free path of the insects also suggest that individuals are on average very weakly coupled, but that they are also tightly bound to the swarm itself. Our results therefore suggest that some attractive interaction maintains cohesion of the swarms, but that this interaction is not as simple as an attraction to nearest neighbours. F rom flocks of birds 1,2 to schools of fish 3,4 to swarms of insects 5-7 , animal aggregations that display collective behaviour appear throughout the animal kingdom 8 . This self-organized, emergent phenomenon has been the subject of intensive modeling for decades, both because it is extremely common in nature and because of its potential utility as a biomimetic control strategy for engineered systems. Low-level interactions between individuals have been shown to allow the percolation of information known by only a few individuals throughout an entire aggregate 9 , and to drive the emergence of collective intelligence such as enhanced sensing 10 . Many types of models of collective animal behaviour have been proposed, ranging from continuum approaches based on partial differential equations 11,12 to cellular automata that specify only simple rules 13 . The most common paradigm, however, is to model the aggregation as a collection of self-propelled, discrete individuals that obey coupled ordinary differential equations 14 . The individuals interact via effective forces that affect their motion just as physical forces would. Typically, these effective forces include a short-range inter-individual repulsion, a longrange attraction, and an intermediate-range tendency for a individual to align its motion with its neighbours 15 . For animal groups that move in a coordinated direction, such as bird flocks, the orientational interaction is often assumed to dominate; for those that stand still, such as insect swarms, the attraction and repulsion are the most important factors 15 . These models are appealing since they are straightforward to simulate, the "forces" that drive the collective behaviour are easily identifiable, and they can produce behaviour that is qualitatively similar to what is observed in nature 16,17 . But simply displaying similar emergent behaviour is not sufficient to claim that a model accurately captures the dynamics of real biological systems 8 ; instead, models must be validated against real empirical data 18,19 . Capturing such data has historically been a significant challenge. To make progress towards validating models of collective animal behaviour, we made quantitative measurements of a canonical animal aggregation: mating swarms of flying insects, also known as leks. (Note that we use the term "swarm" to refer to unpolarized animal groups, rather than simply to groups of insects.) We measured the time-resolved trajectories and kinematics of every individual in several swarms of the flying midge Chironomus riparius. Previously, we reported our measurements of the group properties of the swarms, including their shape and velocity statistics. Here, we probe the statistical properties in more detail to look for signatures of interaction among the midges. Since acceleration is often used as a proxy for social-force information 3,18 , we studied the midge acceleration as a function of the distance to neighboring insects. We found clear evidence for a short-range repulsive inter-individual interaction, a result that we quantitatively confirmed by measuring the spatial distribution of the midges. At larger scales, however, the interpretation of the acceleration statistics is less clear, since on average the midges display an approximately equivalent acceleration in the direction of almost any feature of the swarm. These results suggest that, aside from relatively rare close-range interactions, the midges are on average only weakly coupled. We find further support for this conclusion by estimating the mean free path of the midges and showing that our swarms are rarefied. On the other hand, we also find that the midges are strongly bound to the swarm itself, since the size of the swarm is also on the order of the mean free path. Thus, our results OPEN SUBJECT AREAS: NONLINEAR PHENOMENA BEHAVIOURAL ECOLOGY BIOLOGICAL PHYSICS STATISTICAL PHYSICS
doi:10.1038/srep04766 pmid:24755944 pmcid:PMC3996478 fatcat:tndvalz2g5gqxejdbjrddsxr3e